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JEE Main 2009 (AIEEE) · Beats

Beats question from JEE Main 2009 (AIEEE)

Q67JEE Main 2009 · AIEEEEasy

Beats

Three sound waves of equal amplitudes have frequencies $(v-1),\ v,\ (v+1).$ They superpose to give beats. The number of beats produced per second will be:

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Answer: (b)

Adding the three waves: $y = A\sin(2\pi vt)\left[1 + 2\cos(2\pi t)\right]$
Amplitude $A(1 + 2\cos 2\pi t)$ repeats every 1 s; in each second $|1 + 2\cos 2\pi t|$ has two maxima (at $\cos = 1$ and $\cos = -1$ )
So 2 beats per second: the answer is (b) $2$ .

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